Integrated and Differentiated Spaces of Triangular Fuzzy Numbers

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics, fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. In this paper, we use the triangular fuzzy numbers for matrix domains of sequence spaces with infinite matrices. We construct the new space with triangular fuzzy numbers and investigate to structural, topological and algebraic properties of these spaces.Comment: 10 pages, 17 reference

Taking decisions by using fuzzy models

In the most specialty papers, a mathematical model for establishing the best decisional alternatives is a couple M=(R, K) made up of a matrix R with m lines and n columns and a column vector K with m components. The mathematical modeling of an uncertain information evaluates its most probable value am and the minus possible values as and plus ad. The three real values form an ordered triplet named fuzzy triangular number. A fuzzy model for establishing the best decisional alternative is a couple formed by the results matrix having fuzzy triangular numbers as elements and the importance coefficients vector K. These models, (fuzzy and/or classical) are equivalent models related to a method of hierarchy of decisional alternatives if the two models have the same criteria and alternatives and by using the method to both models, the same hierarchy is obtained.uncertainty, fuzzy triangular numbers, taking decisions, fuzzy models

Program Linier Fuzzy Penuh Dengan Metode Kumar

Fully fuzzy linear programing is part of a crisp linear programming (linear programimg with a number of crisp) which the numbers used are fuzzy numbers. Solving a fully fuzzy linear programming problems by using Kumar method to fuzzy optimal solution and crisp optimal value.. Solving fuzzy optimal solution by Kumar method on triangular fuzzy number to divide into tree objective functions and defuzzification by using ranking function and α - cutting to get crisp optimal solution. This paper discusses about Kumar methods method for solving fully fuzzy linear programming in which fuzzy numbers used are triangular fuzzy numbers

Different strategies to solve fuzzy linear programming problems

Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment In this paper we present methods to solve (i) the fuzzy linear programming problem in which the coefficients of objective function are trapezoidal fuzzy numbers, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers, and (ii) the fuzzy linear programming problem in which the variables are trapezoidal fuzzy variables, the coefficients of objective function and right hand side of the constraints are trapezoidal fuzzy numbers, (iii) the fuzzy linear programming problem in which the coefficients of objective function, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers. Here we use α –cut and ranking functions for ordering the triangular fuzzy numbers and trapezoidal fuzzy numbers. Finally numerical examples are provided to illustrate the various methods of the fuzzy linear programming problem and compared with the solution of the problem obtained after defuzzyfing in the beginning using ranking functions.&nbsp

Modifying Weak Solutions of a Triangular Fuzzy Linear System to Strong Ones

This paper is concerned with the structure of solution space of triangular fuzzy linear systems. The existence of non-triangular fuzzy number solutions for triangular fuzzy linear systems is proved. According to the structure of solution space, an approach of modifying a weak fuzzy number solution of the triangular fuzzy linear system to a strong solution is illustrated. Key Words: Fuzzy numbers; Solution space; Fuzzy linear syste

Program Linier Fuzzy Penuh Dengan Algoritma Multi Objective Linear Programming Menggunakan Metode Level Sum

. Fully Fuzzy Linear Programming (FFLP) is one form of fuzzy linear program that the decision variables, limiting the mark, the objective function coefficients, the coefficient constraints and right hand side constraints are fuzzy numbers. Fuzzy numbers used in FFLP is triangular fuzzy numbers.Several methods have been developed to solve FFLP one method Kumar. This thesis explores the completion FFLP with multi-objective algorithm linear programming (MOLP) and compared with the method of Kumar. FFLP problem will be transformed into a problem MOLP with triangular fuzzy numbers and then completed Level Sum Method

On improving trapezoidal and triangular approximations of fuzzy numbers

AbstractRecently, various researchers have proved that the approximations of fuzzy numbers may fail to be fuzzy numbers, such as the trapezoidal approximations of fuzzy numbers. In this paper, we show by an example that the weighted triangular approximation of fuzzy numbers, proposed by Zeng and Li, may lead to the same result. For filling the gap, improvements of trapezoidal and triangular approximations are proposed. The formulas for computing the two improved approximations are provided. Some properties of the two improved approximations are also proved

First Order Linear Non Homogeneous Ordinary Differential Equation in Fuzzy Environment

In this paper, the solution procedure of a first order linear non homogeneous ordinary differential equation in fuzzy environment is described. It is discussed for three different cases. They are i) Ordinary Differential Equation with initial value as a fuzzy number, ii) Ordinary Differential Equation with coefficient as a fuzzy number and iii) Ordinary Differential Equation with initial value and coefficient are fuzzy numbers. Here fuzzy numbers are taken as Generalized Triangular Fuzzy Numbers (GTFNs). An elementary application of population dynamics model is illustrated with numerical example. Keywords: Fuzzy Ordinary Differential Equation (FODE), Generalized Triangular fuzzy number (GTFN), strong solution